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Propagating Error a Pendulum

  1. Feb 11, 2009 #1
    1. The problem statement, all variables and given/known data

    The length of a string attached to a pendulum is measured with a precision of (+or-)0.2. The time of the oscillation is measured to a precision of (+or-)0.1. How many periods must you measure so that the contribution of the uncertainty in time is smaller than the uncertainty in length, when calculating g?

    2. Relevant equations

    T=2pi(l/g)^(1/2)

    3. The attempt at a solution

    g=((2pi)^2(l+delta:l))/(T+delta:T)^2
    I dont know where to go from here.
    Delta l and T are the error in those measurements.
     
  2. jcsd
  3. Feb 11, 2009 #2
    The next thing to do is assume that the error is really small relative to the actual value.
    [tex]\delta l << l[/tex] and [tex]\delta T << T[/tex]. I think you might have an error in your equation for g:
    [tex] g +\delta g= (2 \pi)^2 \frac{l+\delta l }{(T+\delta T)^2}[/tex] where [tex] \delta g[/tex] is the error in g.
    If you are familiar with calculus then this comes out to:
    [tex]\delta g = |\frac{\partial g}{\partial l}| \delta l + |\frac{\partial g}{\partial T}| \delta T[/tex]
    If you don't have the luxury of calculus we might need to know what relations for uncertainty you are given to clue you in
     
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